BULGING MODES OF CIRCULAR BOTTOM PLATES IN RIGID CYLINDRICAL CONTAINERS FILLED WITH A LIQUID

In this article the free vibrations of the bottom plate of an otherwis e rigid circular cylindrical tank filled with liquid are studied, cons idering only the bulging modes (when the amplitude of the plate displa cement is predominant with respect to that of the free surface). The t ank axis is vertical, thus the free liquid surface is orthogonal to th e tank axis. The liquid is assumed to be inviscid, and the contributio n of the free surface waves to the dynamic pressure on the free liquid surface is neglected. Wet and dry mode shapes of the plate are assume d to be the same, so that the natural frequencies are obtained by usin g the nondimensionalized added virtual mass incremental (NAVMI) factor s and the modal properties of dry plates. This simplifies computations compared to other existing theoretical approaches. NAVMI factors expr ess the nondimensionalized ratio between the reference kinetic energy of the liquid and that of the plate and have the advantage that, due t o their nondimensional form, they can be computed once and for all. Nu merical results for simply supported and clamped bottom plates, as wel l as for supported plates with an elastic moment edge constraint are g iven. For more accurate results, and to exceed the limits of the assum ed modes approach, the Rayleigh-Ritz method is applied and results are compared to those obtained by using the NAVMI factors and other exist ing methods in the literature. (C) 1997 John Wiley & Sons, Inc.